/* -*-c-*-
*
- * $Id: mpbarrett.c,v 1.1 1999/12/10 23:21:59 mdw Exp $
+ * $Id: mpbarrett.c,v 1.10 2004/04/08 01:36:15 mdw Exp $
*
* Barrett modular reduction
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mpbarrett.c,v $
- * Revision 1.1 1999/12/10 23:21:59 mdw
- * Barrett reduction support: works with even moduli.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
#include "mp.h"
mp_shrink(m);
mb->k = MP_LEN(m);
mb->m = MP_COPY(m);
- b = mp_lsl(MP_NEW, MP_ONE, 2 * MPW_BITS * mb->k);
+ b = mp_new(2 * mb->k + 1, 0);
+ MPX_ZERO(b->v, b->vl - 1);
+ b->vl[-1] = 1;
mp_div(&b, 0, b, m);
mb->mu = b;
}
* Returns: The residue of @m@ modulo the number in the reduction
* context.
*
- * Use: Performs an efficient modular reduction. The argument is
- * assumed to be positive.
+ * Use: Performs an efficient modular reduction.
*/
mp *mpbarrett_reduce(mpbarrett *mb, mp *d, mp *m)
if (MP_LEN(m) < k) {
m = MP_COPY(m);
- MP_DROP(d);
+ if (d)
+ MP_DROP(d);
return (m);
}
mp qq;
mp_build(&qq, m->v + (k - 1), m->vl);
q = mp_mul(MP_NEW, &qq, mb->mu);
- q = mp_lsr(q, q, MPW_BITS * (k + 1));
+ if (MP_LEN(q) <= k) {
+ m = MP_COPY(m);
+ if (d)
+ MP_DROP(d);
+ return (m);
+ }
}
/* --- Second stage --- */
mvl = m->vl;
else
mvl = m->v + k + 1;
- r = mp_create(k + 1);
- mpx_umul(r->v, r->vl, q->v, q->vl, mb->m->v, mb->m->vl);
- r->f = (q->f | mb->m->f) & MP_BURN;
- MP_MODIFY(d, k + 1);
+ r = mp_new(k + 1, (q->f | mb->m->f) & MP_BURN);
+ mpx_umul(r->v, r->vl, q->v + k + 1, q->vl, mb->m->v, mb->m->vl);
+ MP_DEST(d, k + 1, r->f);
mpx_usub(d->v, d->vl, m->v, mvl, r->v, r->vl);
- d->f = (m->f | r->f) & MP_BURN;
+ d->f = (m->f | r->f) & (MP_BURN | MP_NEG);
MP_DROP(r);
MP_DROP(q);
MP_DROP(m);
while (MPX_UCMP(d->v, d->vl, >=, mb->m->v, mb->m->vl))
mpx_usub(d->v, d->vl, d->v, d->vl, mb->m->v, mb->m->vl);
- MP_SHRINK(d);
- return (d);
-}
+ /* --- Fix up the sign --- */
-/* --- @mpbarrett_exp@ --- *
- *
- * Arguments: @mpbarrett *mb@ = pointer to Barrett reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$a^e \bmod m$%.
- */
-
-mp *mpbarrett_exp(mpbarrett *mb, mp *d, mp *a, mp *e)
-{
- mpscan sc;
- mp *x = MP_ONE;
- mp *spare = MP_NEW;
-
- a = MP_COPY(a);
- mp_scan(&sc, e);
- if (MP_STEP(&sc)) {
- size_t sq = 0;
- for (;;) {
- mp *dd;
- if (MP_BIT(&sc)) {
- while (sq) {
- dd = mp_sqr(spare, a);
- dd = mpbarrett_reduce(mb, dd, dd);
- spare = a; a = dd;
- sq--;
- }
- dd = mp_mul(spare, x, a);
- dd = mpbarrett_reduce(mb, dd, dd);
- spare = x; x = dd;
- }
- sq++;
- if (!MP_STEP(&sc))
- break;
- }
+ if (d->f & MP_NEG) {
+ mpx_usub(d->v, d->vl, mb->m->v, mb->m->vl, d->v, d->vl);
+ d->f &= ~MP_NEG;
}
- MP_DROP(a);
- if (spare != MP_NEW)
- MP_DROP(spare);
- if (d != MP_NEW)
- MP_DROP(d);
- return (x);
+ MP_SHRINK(d);
+ return (d);
}
/*----- Test rig ----------------------------------------------------------*/
mpbarrett_create(&mb, n);
s = mpbarrett_reduce(&mb, MP_NEW, x);
- if (MP_CMP(s, !=, r)) {
+ if (!MP_EQ(s, r)) {
fputs("\n*** barrett reduction failure\n", stderr);
fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr);
fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
return (ok);
}
-static int vexp(dstr *v)
-{
- mp *m = *(mp **)v[0].buf;
- mp *a = *(mp **)v[1].buf;
- mp *b = *(mp **)v[2].buf;
- mp *r = *(mp **)v[3].buf;
- mp *mr;
- int ok = 1;
-
- mpbarrett mb;
- mpbarrett_create(&mb, m);
-
- mr = mpbarrett_exp(&mb, MP_NEW, a, b);
-
- if (MP_CMP(mr, !=, r)) {
- fputs("\n*** barrett modexp failed", stderr);
- fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
- fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
- fputs("\n e = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
- fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- mp_drop(m);
- mp_drop(a);
- mp_drop(b);
- mp_drop(r);
- mp_drop(mr);
- mpbarrett_destroy(&mb);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return ok;
-}
-
static test_chunk tests[] = {
{ "mpbarrett-reduce", vmod, { &type_mp, &type_mp, &type_mp, 0 } },
- { "mpbarrett-exp", vexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
{ 0, 0, { 0 } }
};